312 Intelligence and Miscellaneous Articles. 



sequently dissolve, when, in the nascent state, they are put into con- 

 tact with potash, in the presence of the salt of potash with which 

 they can combine. 



4. When the oxide is insoluble in the alkalies, it precipitates 

 without redissolving, when the salt which it contains is treated with 

 an excess of alkaline base. This last case happens when the oxide 

 precipitated cannot form a soluble double salt. — Comptes Rendus, 

 Juillet 15, 1850. 



DIRECT DEMONSTRATION OF THE 40TH PROPOSITION OF 

 EUCLID. 



To the Editors of the Philosophical Magazine and Journal. 



North Mall, Cork, 

 Gentlemen, May 13, 1850. 



Permit me to call your attention to the following circumstance in 

 connexion with elementary geometry ; a circumstance rendered im- 

 portant merely by the fact of direct demonstration being generally 

 admitted to be far superior to any indirect demonstration whatsoever*. 

 Euclid, in his treatise on Geometry, proves the 40th proposition of 

 the first book indirectly, which proposition 1 can prove directly, and 

 I think in a simpler and shorter manner than his demonstration, 

 thus : — Ad 



Equal triangles (BAG and EDF) on A" "p 



equal bases and on the same side, are / >--'" j 



between the same parallels. /..--'" \ / 



Join DA, DB and DC. The triangles /./' \/ 



BDC and EDF being on equal bases and B c e s 



between the same parallels (because they have a common altitude 

 (D)), are by the 38th equal ; and as EDF is equal to ABC, BDC 

 must be equal to ABC ; but these being on the same base, are by the 

 39th between the same parallels. Therefore the line AD is parallel 

 to BC or BF. 



Hoping this may prove worthy of insertion in your valuable 

 Journal, 



I have the honour to be, Gentlemen, 



Your obedient Servant, 



John Hennessy, Jun. 



NEW MODE OF PREPARING ETHYALMIN. ETHAMIC ACID. 



M. Strecker remarks, that the excellent researches of M. Wurtz 

 have made known a new class of organic bases, and have thrown 

 much light on the constitution of alkaloids in general. M. Hof- 

 mann has lately discovered a new mode of forming these bases by 



* In Dr. Lardner's seventh edition of the Elements of Euclid, page 20, 

 after showing the distinction between these two kinds of proof, he says, 

 "Consequently, indirect demonstration is never used, except when no 

 direct proof can be had." 



"Examples will be seen in the 14th, 19th, 25th, and 40th propositions of 

 this book." 



